A role of the coefficient of the differential term in qualitative theory of half-linear equations

Title:

A role of the coefficient of the differential term in qualitative theory of half-linear equations

Creator:

Řehák, Pavel

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e89047a3-3555-4e3a-83b2-72a305a2ff0f
uuid:e89047a3-3555-4e3a-83b2-72a305a2ff0f
doi:10.21136/MB.2010.140692

Subject:

half-linear dynamic equation, time scale, transformation, comparison theorem, and oscillation criteria

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The aim of this contribution is to study the role of the coefficient r in the qualitative theory of the equation (r(t)Φ(y ∆))∆+p(t)Φ(y σ ) = 0, where Φ(u) = |u| α−1 sgn u with α > 1. We discuss sign and smoothness conditions posed on r, (non)availability of some transformations, and mainly we show how the behavior of r, along with the behavior of the graininess of the time scale, affect some comparison results and (non)oscillation criteria. At the same time we provide a survey of recent results acquired by sophisticated modifications of the Riccati type technique, which are supplemented by some new observations.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

151-162

Source:

Mathematica bohemica | 2010 Volume:135 | Number:2

Harvested from:

CDK

Metadata only:

false